Abstract
Experiments on leading-edge vortex (LEV) growth and detachment from a plunging profile have been conducted in a free-surface water tunnel. Direct-force and velocity-field measurements have been performed at a Reynolds number of Re = 10,000, a reduced frequency of k = 0.25, and a Strouhal number of St = 0.16, for three varying leading-edge geometries. The leading-edge shape is shown to influence the shear layer feeding the LEV, and thus to some extent the development of the LEV and associated flow topology. This effect in turn influences the arrival time of the rear (LEV) stagnation point at the trailing edge, which, once breached, constitutes a detachment of the LEV. It is found that despite minor phase changes in LEV detachment through leading-edge shape, the position of the trailing edge (chord length) should be chosen as the characteristic length scale for the vortex separation process.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Afanasyev YD (2006) Formation of vortex dipoles. Phys Fluids 18:037,103 doi:10.1063/1.2182006
Baik Y, Bernal L, Granlund K, Ol M (2012) Unsteady force generation and vortex dynamics of pitching and plunging aerofoils. J Fluid Mech 709:37–68
Dabiri JO (2009) Optimal vortex formation as a unifying principle in biological propulsion. Annu Rev Fluid Mech 41:17–33 doi:10.1146/annurev.fluid.010908.165232
DeVoria AC, Ringuette MJ (2011) Vortex formation and saturation for low-aspect-ratio rotating flat-plate fins. Exp Fluids 52(2):441–462 doi:10.1007/s00348-011-1230-z
Doligalski TL, Smith CR, Walker JDA (1994) Vortex interactions with walls. Ann Rev Fluid Mech 26(1):573–616 doi:10.1146/annurev.fl.26.010194.003041
Domenichini F (2011) Three-dimensional impulsive vortex formation from slender orifices. J Fluid Mech 666:506–520 doi:10.1017/S0022112010004994
Foss JF (2004) Surface selections and topological constraint evaluations for flow field analyses. Exp Fluids 37(6):883–898 doi:10.1007/s00348-004-0877-0
Gendrich CP (1999) Dynamic stall of rapidly pitching airfoils: MTV experiments and Navier-Stokes simulations. PhD thesis, Michigan State University
Gharib M, Rambod E, Shariff K (1998) A universal time scale for vortex ring formation. J Fluid Mech 360:121–140
Hunt JCR, Abell CJ, Peterka JA, Woo H (1978) Kinematical studies of the flows around free or surface-mounted obstacles; applying topology to flow visualization. J Fluid Mech 86:179–200 doi:10.1017/S0022112078001068
Nudds RL, Taylor GK, Thomas ALR (2004) Tuning of strouhal number for high propulsive efficiency accurately predictes how wingbeat frequency and stroke amplitude relate and scale with size and flight speed in birds. Proc R Soc B 271:2071–2076
Pedrizzetti G (2010) Vortex formation out of two-dimensional orifices. J Fluid Mech 655:198–216 doi:10.1017/S0022112010000844
Perry AE, Chong MS (1987) A description of eddying motions and flow patterns using critical-point concepts. Annu Rev Fluid Mech 19:125–155 doi:10.1146/annurev.fl.19.010187.001013
Rival DE, Prangemeier T, Tropea C (2009) The influence of airfoil kinematics on the formation of leading-edge vortices in bio-inspired flight. Exp Fluids 46:823–833 doi:10.1007/s00348-008-0586-1
Rival DE, Manejev R, Tropea C (2010) Measurement of parallel blade-vortex interaction at low reynolds numbers. Exp Fluids 49:89–99 doi:10.1007/s00348-009-0796-1
Sattari P, Rival D, Martinuzzi R, Tropea C (2012) Growth and separation of a start-up vortex from a two-dimensional shear layer. Phys Fluids 24:107,102 doi:10.1063/1.4758793
Savitzky A, Golay MJE (1964) Smoothing and differentiation of data by simplified least squares procedures. Anal Chem 36(8):1627–1639 doi:10.1021/ac60214a047
Taylor GK, Nudds RL, Thomas A (2003) Flying and swimming animals cruise at a strouhal number tuned for high power efficiency. Nature 425:707–710
Triantafyllou MS, Triantafyllou GS, Gopalkrishnan R (1991) Wake mechanics for thrust generation in oscillating foils. Phys Fluids A 3:2835–2838
Acknowledgments
This project was funded by the Natural Science and Engineering Research Council of Canada (NSERC) and the Deutsche Forschungsgemeinschaft (DFG). The authors gratefully thank Prof. John Foss for the fruitful discussions regarding the topology of this flow.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rival, D.E., Kriegseis, J., Schaub, P. et al. Characteristic length scales for vortex detachment on plunging profiles with varying leading-edge geometry. Exp Fluids 55, 1660 (2014). https://doi.org/10.1007/s00348-013-1660-x
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00348-013-1660-x